Environment-dependent dissipation in quantum Brownian motion

Abstract

The dissipative dynamics of a quantum Brownian particle is studied for different types of environment. We derive analytic results for the time evolution of the mean energy of the system for Ohmic, sub-Ohmic and super-Ohmic environments, without performing the Markovian approximation. Our results allow to establish a direct link between the form of the environmental spectrum and the thermalization dynamics. This in turn leads to a natural explanation of the microscopic physical processes ruling the system time evolution both in the short-time non-Markovian region and in the long-time Markovian one. Our comparative study of thermalization for different environments sheds light on the physical contexts in which non-Markovian dissipation effects are dominant.

Decoherence control in different environments

“…This is in contrast with the dynamics of the heating function where nonMarkovian oscillations, indicating an exchange of energy between the system and the environment, characterize the r ≪ 1 regime, for all types of reservoirs [4].…”

“…These types of reservoirs have been recently engineered in the trapped ion context [24] and a theoretical comparative study of the heating function for these reservoirs types has been presented in Ref. [4]. The spectral distribution…”

“…Such a process is faster and faster the more macroscopic the initial state is [3]. The details of the dynamics of the decoherence process depend, among other things, on the structure of the environment [4].…”

Continuous-variable quantum probes for structured environments

“…(5c), by choosing a coarse-grained dynamical regime ω 0 t 1 [15,27]. The secularly approximated CM of the evolved probe state reads…”

“…The interaction between a quantum system and its harmonic environment, usually assumed in thermal equilibrium, is, in general, frequency-dependent and may be described in terms of the spectral density function of the environment itself, which rules the range of frequencies accessible to the open system under investigation, and determines its rates of dissipation and decoherence [25][26][27][28]. With the advent of state engineering [29,30], it is possible to build a rich variety of struc- * Electronic address: matteo.bina@gmail.com tured environments and/or to simulate complex open quantum systems dynamics.…”